Polarization transformer

ABSTRACT

A method for fabricating a transformer of linearly polarized light to elliptically polarized light is presented. The method involves twisting a birefringent fiber through angles that depend on the polarization desired. This technique obviates the need to splice fibers, as in common approaches. In the final step of the method, the polarization can be fine tuned by heating the fiber to cause the core of the fiber to diffuse into the cladding. Also, methods and systems are presented to transform substantially polarized light to substantially randomly polarized light.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims priority to the following U.S.patent applications. U.S. provisional patent application, serialapplication No. 60/119,999, filed on Feb. 11, 1999; U.S. provisionalpatent application, serial application No. 60/120,000, filed on Feb. 11,1999; U.S. provisional patent application, serial application No.60/133,357, filed on May 10, 1999; and U.S. provisional patentapplication, serial application No. 60/134,154, filed on May 14, 1999.This application is also based upon U.S. application entitled CurrentSensor, invented by Richard Dyott, which has been filed concurrentlywith the present application on Jun. 22, 1999. All of the aforementionedapplications are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This application relates to optical devices that transform light betweenlinearly and elliptically polarized states.

2. Description of Related Art

Devices that transform linearly polarized light to circularly polarizedlight and the reverse are known in the literature. To make such opticaldevices, one may use one birefringent fiber with two beams of light ofequal frequency and amplitude (or, equivalently, one beam that is thevector sum of these two beams). If the two beams are propagatedperpendicular to an optic axis, circularly polarized light may result.Alternatively, linearly polarized light may be transformed to circularlypolarized light by using one beam and two fibers.

In practice, constructing a single-beam transformer of linearly tocircularly polarized light involves first starting with a length oftransforming fiber greater than a predetermined length, and performingseveral iterations of cutting and measuring polarization until thepolarization is deemed to be circular to within some specification.Needless to say, this is a tedious and lengthy procedure requiring lotsof guesswork.

SUMMARY OF THE INVENTION

A transformer of polarized light comprising a birefringent fiber whichis twisted through an angle into a corkscrew shape at an appropriatedistance from an end of the fiber is presented herein; the angle anddistance are so chosen that linearly polarized light entering the otherend of the fiber exits the fiber elliptically polarized. In variousembodiments, the angle is approximately π/4 radians, or an odd multiplethereof, and the distance is approximately one quarter of a beatlength,or an odd multiple thereof. The transformer of polarized light mayinclude an optical fiber twisted about a central axis runningtherethrough wherein the fiber is characterized by the absence ofspliced sections.

A method of fabricating a transformer of polarized light comprisingtwisting a birefringent fiber through an angle to produce a corkscrewshape is also presented; twisting a birefringent fiber may includetwisting the fiber through an angle of approximately π/4 radians, or anodd multiple thereof, and twisting the fiber at a distance ofapproximately one quarter of a beatlength, or an odd multiple thereof,from an end of the fiber.

A method of fabricating a transformer of polarized light is alsopresented which may include heating a birefringent fiber, having a coreand a cladding, so as to cause the core to diffuse into the cladding,and thereby changing the state of polarization of light that may exitthe fiber. The method may further include previously twisting the fiberthrough an angle to produce a corkscrew shape. (In one embodiment, thisangle is π/4 radians.) Twisting the fiber includes twisting the fiber ata distance of approximately one quarter of a beatlength from an end ofthe fiber.

Also presented is a method of transforming substantially linearlypolarized light into substantially circularly polarized light includingtwisting a birefringent fiber through an angle of π/4 radians to producea corkscrew shape at a distance of approximately one quarter of abeatlength from an end of the fiber; shining substantially linearlypolarized light through the other end of the fiber; and fine tuning thepolarization of the light exiting the fiber by heating the fiber so asto cause the core to diffuse into the cladding, until the light issubstantially circularly polarized. The twist in the fiber can beaccomplished by heating the fiber before, during, or after the twisting.

The invention further includes a transformer of polarized lightcomprising a birefringent fiber. The fiber has a first end through whichthe polarized light enters and a second end through which light exits.The fiber is also twisted through an angle into a corkscrew shape at anappropriate distance from the second end, the angle and distance sochosen that polarized light entering the first end exits the second endrandomly polarized. The appropriate length may be greater than adecoherence length.

Also presented is a method of transforming substantially polarized lightinto substantially randomly polarized light including twisting abirefringent fiber, having a first end through which the substantiallypolarized light enters and a second end through which the substantiallyrandomized light exits, through an angle of π/4 radians to produce acorkscrew shape at a distance of at least one decoherence length fromthe second end of the fiber; and shining substantially polarized lightthrough the first end of the fiber to allow substantially randomlypolarized light to exit the second end.

Also presented is a method of transforming substantially linearlypolarized light into substantially circularly polarized light comprisingtwisting a birefringent fiber, having two ends, about its central axisthrough an angle approximately equal to an odd multiple of π/4 radians,at a distance of slightly more than odd multiple of one quarter of abeatlength from a first end of the fiber, shining substantially linearlypolarized light through a second end of the fiber, and fine turning thepolarization of the light exiting the first end of the fiber by heatingthe fiber between the twist and the first end, so as to cause the coreto diffuse into the cladding, until the exiting light is substantiallycircularly polarized. The odd multiple of one quarter of a beatlengthmay be 1. The odd multiple of π/4 radians may be 1. The birefringentfiber may be twisted while being heated near the location of the twistor after having been heated near the location of the twist.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates the conventional method of fabricating a transformerof linearly to circularly polarized light by splicing two fibers thatare properly oriented.

FIG. 2 is a schematic of a twisted fiber of the present invention thatobviates the need to splice fibers together.

FIG. 3 illustrates how fine tuning of the polarization can be achievedby heating the fiber to cause diffusion of the core into the cladding.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

It is often desirable to transform the polarization of a beam of lightfrom one state to another. For this purpose optical devices have beenfabricated that input linearly polarized light and output ellipticallypolarized light. These devices typically function by causing one of twoincident linearly polarized light beams to lag behind the other by apre-selected phase difference. Altering the relative phase of the twoincident beams has the effect of changing the state of polarization ofthe light that exits the optical device. Before considering how thesedevices of the prior art perform the transformation of linearly toelliptically polarized light and before presenting the detaileddescription of the preferred embodiment of the present invention, itwill be useful to first recall how elliptically polarized light arises.

Two orthogonal electric fields, E_(x) and E_(y), both propagating in thez direction can be described by the following two equations

E _(x) =iE _(0x)cos(kz−ωt)  (1)

and

E _(y) =j E _(0y)cos(kz−ωt+δ),  (2)

where i and j are unit vectors in the x and y directions, k is thepropagation number, ω is the angular frequency, and δ is the relativephase difference between the two modes. The total electric field E isjust given by the vector sum E_(x)+E_(y). An observer standing at afixed point on the z-axis and measuring the components E_(x) and E_(y)of the total electric field simultaneously would find that thesecomponents would fall on the curve

 (E _(x) /E _(0x))²+(E _(y) /E _(0y))²−2(E _(x) /E _(0x)) (E _(y) /E_(0y))cos δ=sin²δ.  (3)

Equation (3) is the well known equation of an ellipse making an angle αwith the (E_(x), E_(y))-coordinate system, where

tan 2α=(2E _(0x) E _(0y) cos δ)÷(E _(0x) ² −E _(0y) ²).  (4)

Hence, E corresponds to elliptically polarized light. From Equation (3)can be seen that the phase difference δ dictates some of thecharacteristics of the ellipse. For example, if δ were equal to an evenmultiple of 2π (i.e., if E_(x) and E_(y) are in phase), then Equation(3) reduces to E_(y)=(E_(0y)/E_(0x))E_(x), which is the equation of astraight line; in that case, E is linearly polarized. On the other hand,if δ is equal to ±π/2, ±3π/2, ±5π/2, . . . , and assumingE_(0x)=E_(0y)=E₀, Equation (3) reduces to E_(0x) ²+E_(0y) ²=E₀ ², whichis the equation of a circle. In that case, E is circularly polarized. Ofcourse, linearly and circularly polarized light are just special casesof elliptically polarized light, a line and a circle being special typesof ellipses.

From the above considerations, it is clear that if two perpendicularmodes of light with equal amplitudes, such as that described byEquations (1) and (2) with E_(0x)=E_(0y), enter an optical device, andproceed to exit the device with a phase shift of π/2, the result wouldbe circularly polarized light. Typical optical devices that serve totransform linearly polarized light to circularly polarized light work onthis principle.

For example, birefringent light fibers are anisotropic meaning that theydo not have the same optical properties in all directions. Such fibershave the following properties: If two linearly polarized light beams aretraveling along the fiber, or along the z axis, and furthermore one beamis polarized along the y axis and the other along the x axis, then,while the beam polarized along the y axis will travel at a speed v, theother beam that is polarized along the x axis will have a differentspeed. (In a birefringent fiber, the term “optic axis” may refer toeither the fast or the slow axis, which are taken here to be the x and yaxes, both perpendicular to the propagation axis, taken here to be the zaxis.) Such two beams moving perpendicular to an optic axis may enterthe fiber in phase, but because of their disparate speeds will exit witha non-zero phase difference δ. The result, as was seen above, iselliptically polarized light.

In the time, Δt, that it takes the faster moving beam to traverse thebirefringent fiber, the faster moving beam, with speed v_(fast), willoutpace the slower moving beam, with speed v_(slow), by a distance(v_(fast)−v_(slow))Δt. This last mentioned distance contains(v_(fast)−v_(slow))Δt/λ_(slow) waves of the slower moving beam havingwavelength λ_(slow). Noting that Δt=L/v_(fast), where L is the fiberlength, the phase difference between the two beams is given by

δ=2π(v _(fast) −v _(slow))L/(λ_(slow) v _(fast)).  (5)

This last equation can be rewritten by substituting

v _(fast) =λ _(fast)ν,  (6)

and

v _(slow)=λ_(slow)ν,  (7)

where ν is the common frequency of the slow and fast beams, to yield

 L=(δ/2π) (1/λ_(slow)−1/λ_(fast))⁻¹  (8)

This last equation makes clear that one can tailor a birefringent fiberto act as a transformer of linearly polarized light into ellipticallypolarized light simply by choosing the correct length, L, of fiber,although this length depends on the frequency of the light throughEquations (7) and (8). The length of fiber that results in a phasedifference of 2π and that therefore leaves the polarization unchanged isknown as a beatlength, denoted by L_(b), and will play a role in thediscussion below.

The above discussion may be generalized to show that if instead ofpurely monochromatic light, light containing a spectrum of wavelengthsis employed, birefringent fibers may be employed to convert suchlinearly polarized light to elliptically polarized light, where thedegree of polarization of the output light decreases with increasingwidth of the input spectrum. In addition, the above discussion may begeneralized to show that the polarization transformer will convertelliptically polarized light into linearly polarized light, if the lightpropagates through the fiber in the reverse direction.

To make optical devices that transform linearly polarized light intoelliptically polarized light, one may use a birefringent fiber with twobeams of light of equal frequency and amplitude (or, equivalently, onebeam that is the vector sum of these two beams, since, as is known inthe art, a single beam of linearly polarized light may be described asthe vector sum of two beams, each with a single linear polarizationcomponent; conversely, two linearly polarized beams may be vector summedinto a single linearly polarized beam). Alternatively, polarizationcomponents of unequal amplitude may be employed. As was discussed above,if the two beams are propagated perpendicular to the x axis, and theirpolarizations are along the x and y axes, elliptically polarized lightmay result. Alternatively, linearly polarized light may be transformedto circularly polarized light by using one beam and two birefringentfibers, one of which is rotated by 45 degrees with respect to the otherabout the common propagation axis of the fibers, and of length L_(b)/4.

Referring to FIG. 1, such a single-beam transformer of linearlypolarized light to circularly polarized light may be constructed byfusing two silica or glass birefringent fibers. One of these fibers isthe transmitting fiber 2 that delivers light to a second birefringentfiber known as the transforming fiber 4. The transforming fiber 4 is cutto a length of L_(b)/4. In addition, the relative orientation of the twofibers is chosen so that the transmitting fiber 2 is rotated π/4 radianswith respect to the transforming fiber, about the common propagationaxis of the two fibers, as indicated by the transmitting fiber crosssection 6 and the transforming fiber cross section 8. Such a splicingoperation may be done with a commercially available fusion splicer.However, any misalignment of the fibers results in some light being lostat the splice 10. Moreover, as Equation 5 makes clear, errors in thephase difference δ grow linearly with errors in the fiber length L. Inpractice, constructing a single-beam transformer of linearly tocircularly polarized light involves first starting with a length oftransforming fiber 4 greater than L_(b)/4, and performing severaliterations of cutting and measuring polarization of light emerging fromthe end of the transforming fiber until the polarization is deemed to becircular to within some specification. Needless to say, this is atedious and lengthy procedure requiring lots of guesswork.

The present invention resolves some of the aforementioned problems bypresenting an alternate method of fabricating a single-beam transformerof polarized light. Referring to FIG. 2, instead of splicing two fibersoffset by π/4 radians, in the method of the present invention a singlebirefringent fiber 12 is twisted about its central axis by this angle.In an alternate embodiment, the fiber may be twisted by an angle of anodd multiple of π/4 radians. The twist 14 in the fiber may beaccomplished by heating the birefringent fiber 12 using arc electrodes16, or other local heat source known to those of skill in the art. Thismay be done while applying torsion to twist the fiber, using methodsknown to those of skill in the art.

Referring to FIG. 3, in lieu of the tedious iterations of cutting andmonitoring, in the method of the present invention, fine tuning isachieved by heating the portion of the fiber beyond the twist with adiffusing arc 26 produced by arc electrodes 22, or other local heatsource known to those of skill in the art, to cause diffusion of thefiber core into the cladding. The heating can continue until apolarization monitor 24 indicates that the right polarization state isachieved. The effect of the diffusion is to expand the fields of thefiber modes and so reduce the effective difference v_(fast)−v_(slow),thereby increasing the beat length.

The steps of twisting and diffusing are conceptually independent, andeach can be used profitably to make transformers of linearly toelliptically polarized light. Varying the angle through which thebirefringent fiber 12 is twisted is tantamount to varying the amplitudesE_(0x) and E_(0y) of Equation (3) and results in different states ofelliptically polarized light. The step of diffusing, on the other hand,can be used any time some fine tuning of the polarization is required.For example, after splicing two fibers of appropriate length accordingto conventional methods, the state of polarization can be fine tuned bycausing the core to diffuse into the cladding.

One can also fabricate a transformer using one birefringent fiber andtwo beams of linearly polarized light. If the two beams are propagatedperpendicular to the x axis, and their polarizations are along the x andy axes, elliptically polarized light results. After cutting the singlefiber to an appropriate length, fine tuning of the sought-afterpolarization can be achieved by heating the fiber to cause diffusion ofthe core into the cladding as mentioned above.

The present invention presents a more convenient method to fabricate atransformer of polarized light. The first step of the method obviatesthe need to splice a transmitting fiber 2 to a transforming birefringentfiber 4 of length L_(b)/4 with the aim of producing a transformer oflinearly to circularly polarized light. Instead, a convenient length ofa birefringent fiber 12 is heated to the softening point of the glassand then twisted through an angle of approximately π/4 radians. In someembodiments, an angle approximately equal to an odd multiple of π/4 maybe employed. The sense of the output polarization (i.e., whether thelight is right- or left-circularly polarized) may be determined by theorientation of the input light's polarization vector with respect to thedirection of the twist. In a preferred embodiment, the twisting shouldoccur over as short a length as possible. Employing a twist rather thana splice between two fibers offset by an angle keeps optical losses low.What losses do occur may be scarcely measurable in practice.

In the next step of the invention, fine tuning is performed in thefollowing manner. First, the birefringent fiber 12 is cut so that itslength from the twist 14 to the end of the fiber is slightly larger thanL_(b)/4. In an alternate embodiment, the length of the fiber after thetwist may be approximately equal to an odd multiple of L_(b)/4. Thetwisted birefringent fiber 12 is positioned between the arc electrodes22 of a fiber fusion splicer. A diffusing arc 26 may be struck at acurrent lower than that used for splicing in order to raise thetemperature of the birefringent fiber 12 to a point below its meltingpoint, but where the fiber core begins to diffuse into the cladding. Theeffect of the diffusion is to expand the fields of the fiber modes andso reduce the effective birefringence. The light emerging from thetransformer is monitored during this operation with the use of apolarization monitor 24, and diffusion is stopped when the light iscircularly polarized. FIG. 3 shows the arrangement.

Although what was described above is a preferred method for fabricatinga single-beam transformer of linearly to circularly polarized light bythe steps of twisting and diffusing, it should be understood that thesetwo steps are independent and each may be profitably used individually.For example, to form a single-beam transformer of linearly to circularlypolarized light, a single birefringent fiber can be twisted as describedabove, and then fine tuned not by the preferred method of diffusing, butby a conventional method of iterations of cutting the fiber to anappropriate length and monitoring the polarization.

Alternatively, two fibers may be spliced together as in usualapproaches. The transforming fiber would then be cut to a length ofapproximately L_(b)/4. However, unlike the usual methods that then finetune by iterations of cutting and monitoring, the tuning could proceedby causing the core to diffuse into the cladding, as described above.

Finally, instead of twisting a birefringent fiber through an angle ofπ/4 radians, which corresponds to choosing E_(0x)=E_(0y) in Equation(3), the fiber could be twisted through varying angles. This would beeffectively equivalent to varying the amplitudes E_(0x) and E_(0y). Ascan be seen from this equation, even if the length of the fiber wouldlead to a phase difference of π/4 radians, the result would generally beelliptically polarized light that is non-circular.

The above methods have involved fabricating a single-beam transformer oflinearly to circularly, or in the case where the twisting angle is notπ/4 radians or an odd multiple thereof, elliptically polarized light. Asmentioned above, one can also build a transformer using one birefringentfiber and two beams of orthogonally linearly polarized light (of course,two beams of superposed light is equivalent to a single beam equal tothe vector sum of the two constituent beams). If the two beams arepropagated along the z axis perpendicular to the x axis, and theirpolarizations are along the x and y axes, elliptically polarized lightmay result. According to Equations 3, 4, and 5, the type of ellipticallypolarized light that results depends on the length of the fiber, L.After cutting a birefringent fiber to an appropriate length, fine tuningof the polarization can proceed by diffusing the core into the cladding,as described above.

In a related application of the present invention, the twistingprocedure described above may also be used to construct depolarizingfiber. If light having a band of different frequencies enters a fiberwith the type of twist described above, after traveling a certain lengthknown as the decoherence length (see Richard B. Dyott, Elliptical FiberWaveguides, Artech House, which is incorporated herein by reference),the emergent light will be randomly polarized even if the light enteringthe fiber was polarized. Such randomly polarized light may have variousapplications known to those of ordinary skill in the art.

The transformer of linearly to circularly polarized light describedabove can be used in a current sensor exploiting the Faraday Effect in aSagnac interferometer. A main feature of a Sagnac interferometer is asplitting of a beam of light into two beams. By using mirrors or opticalfibers, both beams of light are made to traverse at least one loop, butin opposite directions. At the end of the trip around the loop, bothbeams are recombined thus allowing interference to occur. Anydisturbance that affects one or both beams as they are traversing theloop has the potential to alter the interference pattern observed whenthe beams recombine. Rotating the device is the traditional disturbanceassociated with Sagnac's name. Another disturbance, giving rise to theFaraday Effect, involves applying an external magnetic field to themedium that forms the loop through which the light travels. Under theinfluence of such a field, the properties of the light-transmittingmedium forming the loop are altered so as to cause a change in thedirection of polarization of the light. In turn, this change in thedirection of polarization results in a change in the interferencepattern observed. These types of disturbances that give rise to amodification in the observed interference pattern are known asnon-reciprocal disturbances. They are so-called because, unlikereciprocal effects in which the change produced in one beam cancels withthat produced in the other, the changes produced in the two beamsreinforce to yield a modification in the resultant interference pattern.

There is therefore in place a technique for measuring the currentthrough a conductor: as a consequence of the Biot-Savart Law, aninfinitely long conducting wire, for example, carrying a current i,gives rise to a magnetic field whose magnitude at a distance R from thewire is μ₀i÷(2πR), where uo is the permeability of free space. If theSagnac interferometer described above is immersed in this magneticfield, the properties of the fiber that composes the coil will change soas to affect the interference pattern observed. Thus, from the change inthis pattern, the current i can be inferred. Similar current sensors areknown in the prior art, e.g., Interferometer device for measurement ofmagnetic fields and electric current pickup comprising a device, U.S.Pat. No. 4,560,867, naming Papuchon; Michel; Arditty; Herve; Puech;Claude as inventors, which is incorporated by reference herein. Thedesign of current sensors is similar to that of fiber optic rotationsensors of the type that appears in Fiber Optic Rotation Sensor orGyroscope with Improved Sensing Coil, U.S. Pat. No. 5,552,887, namingDyott, Richard B. as inventor, which is incorporated by referenceherein.

It will be understood by those of ordinary skill in the art, thatperfectly linearly or circularly polarized light may be an idealizationthat can not be realized. I.e., in practice, there may existuncontrollable factors that give rise to some deviations from perfectlylinearly or circularly polarized light. Therefore, it should beunderstood that when reference is made to linearly or circularlypolarized light the meaning of these terms should be taken to meaneffectively or approximately linearly or circularly polarized light.

While the invention has been disclosed in connection with the preferredembodiments shown and described in detail, various modifications andimprovements thereon will become readily apparent to those skilled inthe art. Accordingly, the spirit and scope of the present invention isto be limited only by the following claims.

What is claimed is:
 1. A method of transforming substantially linearlypolarized light into substantially circularly polarized light comprisinga) twisting a birefringent fiber through an angle of π/4 radians toproduce a corkscrew shape at a distance of one quarter of a beatlengthfrom an end of the fiber; b) shining substantially linearly polarizedlight through an end of the fiber furthest from the twist; and c) finetuning the substantially circularly polarized light exiting the fiber byheating the fiber so as to cause the core to diffuse into the cladding.2. A method of transforming substantially linearly polarized light intosubstantially circularly polarized light as in claim 1 wherein twistinga birefringent fiber occurs after heating the fiber.
 3. A method oftransforming substantially polarized light into substantially randomlypolarized light comprising a) twisting a birefringent fiber, said fiberhaving a first end through which the substantially polarized lightenters and a second end through which the substantially randomized lightexits, through an angle of π/4 radians about a central axis runningtherethrough, at a distance of at least one decoherence length from thesecond end of the fiber; and b) shining substantially polarized lightthrough the first end of the fiber to allow substantially randomlypolarized light to exit the second end.
 4. A method of transformingsubstantially linearly polarized light into substantially circularlypolarized light comprising a) twisting a birefringent fiber, having twoends, about its central axis through an angle approximately equal to anodd multiple of π/4 radians, at a distance of slightly more than an oddmultiple of one quarter of a beatlength from a first end of the fiber;b) shining substantially linearly polarized light through a second endof the fiber; and c) fine tuning the polarization of the light exitingthe first end of the fiber by heating the fiber between the twist andthe first end, so as to cause the core to diffuse into the cladding,until the exiting light is substantially circularly polarized.
 5. Themethod of transforming substantially linearly polarized light intosubstantially circularly polarized light of claim 4, wherein the oddmultiple of π/4 radians is
 1. 6. The method of transformingsubstantially linearly polarized light into substantially circularlypolarized light of claim 4, wherein the odd multiple of one quarter of abeatlength is
 1. 7. The method of transforming substantially linearlypolarized light into substantially circularly polarized light of claim6, wherein the odd multiple of π/4 radians is
 1. 8. The method oftransforming substantially linearly polarized light into substantiallycircularly polarized light of claim 4, wherein the birefringent fiber istwisted while being heated near the location of the twist.
 9. The methodof transforming substantially linearly polarized light intosubstantially circularly polarized light of claim 4, wherein thebirefringent fiber is twisted after having been heated near the locationof the twist.